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Chapitre D'ouvrage Année : 2015

Knot theory and matrix integrals

Résumé

The large size limit of matrix integrals with quartic potential may be used to count alternating links and tangles. The removal of redundancies amounts to renormalizations of the potential. This extends into two directions: higher genus and the counting of "virtual" links and tangles; and the counting of "coloured" alternating links and tangles. We discuss the asymptotic behavior of the number of tangles as the number of crossings goes to infinity.

Dates et versions

hal-00526788 , version 1 (15-10-2010)

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Citer

P. Zinn-Justin, J. -B. Zuber. Knot theory and matrix integrals. The Oxford Handbook of Random Matrix Theory Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco, 2015. ⟨hal-00526788⟩
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